Two-body propagators with dynamic effective interactions in a many-fermion medium: II. s-Channel

In open-shell nuclear structure calculations collective excitations of the closed-shell core play an important role. When the energies of these excitations are comparable to the spread of energies in the model space a dynamic treatment of the core states is essential. In a Green function formulation dynamic core states, represented by particle-hole phonons, are included in the effective interaction of the s-channel integral equation for the fourfermion vertex function Γ. The solution of the equation is obtained analytically and from it the s-channel two-body propagator K is calculated. The structure of the propagator K reveals that, in addition to poles corresponding to the normal shell model states, many new poles of K are obtained. These correspond to two-particle-n-phonon configurations. Furthermore, it is shown that, due to the phonons, correlations of the ground state are induced in the calculation of the propagator K. The difference between these correlations and the well-known particle-particle-RPA correlations also included in the formalism is pointed out. The expressions derived can easily be handled numerically. In the calculations the physical states of single-particle and single-hole nuclei can be incorporated by an appropriate dressing of the single-fermion Green function.